This chapter is from the book

This chapter is from the book

In Chapter 9 we delved into advanced 2D graphics programming. In this chapter we will explore GDI+ transformations. A transformation is a process that changes graphics objects from one state to another. Rotation, scaling, reflection, translation, and shearing
are some examples of transformation. Transformations can be applied not only to graphics shapes, curves, and images, but even
to image colors.

In this chapter we will cover the following topics:

The basics of transformation, including coordinate systems and matrices

Global, local, and composite transformations

Transformation functionality provided by the Graphics class

Transformation concepts such as shearing, rotation, scaling, and translation

Any drawing process involves a source and a destination. The source of a drawing is the application that created it, and the
destination is a display or printer device. For example, the process of drawing a simple rectangle starts with a command telling
GDI+ to draw on the screen, followed by GDI+ iterating through multiple steps before it finally renders a rectangle on the
screen. In the same way, transformation involves some steps before it actually renders the transformed object on a device.
These steps are shown in Figure 10.1, which shows that GDI+ is responsible for converting world coordinates to page coordinates and device coordinates before
it can render a transformed object.

10.1 Coordinate Systems

Before we discuss transformations, we need to understand coordinate systems. GDI+ defines three types of coordinate spaces:
world, page, and device. When we ask GDI+ to draw a line from point A (x1, y1) to point B (x2, y2), these points are in the world coordinate system.

Before GDI+ draws a graphics shape on a surface, the shape goes through a few transformation stages (conversions). The first
stage converts world coordinates to page coordinates. Page coordinates may or may not be the same as world coordinates, depending
on the transformation. The process of converting world coordinates to page coordinates is called world transformation.

The second stage converts page coordinates to device coordinates. Device coordinates represent how a graphics shape will be
displayed on a device such as a monitor or printer. The process of converting page coordinates to device coordinates is called
page transformation. Figure 10.2 shows the stages of conversion from world coordinates to device coordinates.

In GDI+, the default origin of all three coordinate systems is point (0, 0), which is at the upper left corner of the client
area. When we draw a line from point A (0, 0) to point B (120, 80), the line starts 0 pixels from the upper left corner in
the x-direction and 0 pixels from the upper left corner in the y-direction, and it will end 120 pixels over in the x-direction and 80 pixels down in the y-direction. The line from point A (0, 0) to point B (120, 80) is shown in Figure 10.3.

Drawing this line programmatically is very simple. We must have a Graphics object associated with a surface (a form or a control). We can get a Graphics object in several ways. One way is to accept the implicit object provided by a form’s paint event handler; another is to
use the CreateGraphics method. Once we have a Graphics object, we call its draw and fill methods to draw and fill graphics objects. Listing 10.1 draws a line from starting point A (0, 0) to ending point B (120, 80). You can add this code to a form’s paint event handler.

Listing 10.1 Drawing a line from point (0, 0) to point (120, 80)

Figure 10.3 shows the output from Listing 10.1. All three coordinate systems (world, page, and device) draw a line starting from point (0, 0) in the upper left corner of
the client area to point (120, 80).

Now let’s change to the page coordinate system. We draw a line from point A (0, 0) to point B (120, 80), but this time our
origin is point (50, 40) instead of the upper left corner. We shift the page coordinates from point (0, 0) to point (50, 40).
The TranslateTransform method of the Graphics class does this for us. We will discuss this method in more detail in the discussion that follows. For now, let’s try the
code in Listing 10.2.

Listing 10.2 Drawing a line from point (0, 0) to point (120, 80) with origin (50, 40)

Figure 10.4 shows the output from Listing 10.2. The page coordinate system now starts at point (50, 40), so the line starts at point (0, 0) and ends at point (120, 80).
The world coordinates in this case are still (0, 0) and (120, 80), but the page and device coordinates are (50, 40) and (170,
120). The device coordinates in this case are the same as the page coordinates because the page unit is in the pixel (default)
format.

Figure 10.4. Drawing a line from point (0, 0) to point (120, 80) with origin (50, 40)

What is the difference between page and device coordinates? Device coordinates determine what we actually see on the screen.
They can be represented in many formats, including pixels, millimeters, and inches. If the device coordinates are in pixel
format, the page coordinates and device coordinates will be the same (this is typically true for monitors, but not for printers).

The PageUnit property of the Graphics class is of type GraphicsUnit enumeration. In Listing 10.3 we set the PageUnit property to inches. Now graphics objects will be measured in inches, so we need to pass inches instead of pixels. If we draw
a line from point (0, 0) to point (2, 1), the line ends 2 inches from the left side and 1 inch from the top of the client
area in the page coordinate system. In this case the starting and ending points are (0, 0) and (2, 1) in both world and page
coordinates, but the device coordinate system converts them to inches. Hence the starting and ending points in the device
coordinate system are (0, 0) and (192, 96), assuming a resolution of 96 dots per inch.

Listing 10.3 Setting the device coordinate system to inches

g.PageUnit = GraphicsUnit.Inch;
g.DrawLine(Pens.Black, 0, 0, 2, 1);

Figure 10.5 shows the output from Listing 10.3. The default width of the pen is 1 page unit, which in this case gives us a pen 1 inch wide.

Now let’s create a new pen with a different width. Listing 10.4 creates a pen that’s 1 pixel wide (it does so by dividing the number of pixels we want—in this case 1—by the page resolution,
which is given by DpiX). We draw the line again, this time specifying a red color.

Listing 10.4 Using the GraphicsUnit.Inch option with a pixel width

Figure 10.6. Drawing with the GraphicsUnit.Inch option and a pixel width

We can also combine the use of page and device coordinates. In Listing 10.5 we transform page coordinates to 1 inch from the left and 0.5 inch from the top of the upper left corner of the client area.
Our new page coordinate system has starting and ending points of (1, 0.5) and (3, 1.5), but the device coordinate system converts
them to pixels. Hence the starting and ending points in device coordinates are (96, 48) and (288, 144), assuming a resolution
of 96 dots per inch.